Question

Помогите прошу вас, даю 20 баллов
докажите тождество (m^2/m+5-m3/m2+10m+25):(m/m+5-m^2/m^2-25)=5m-m^2/m+5

Answer 1

$left( frac{m^2}{m+5}- frac{m^3}{m^2+10m+25}right):left( frac{m}{m+5}- frac{m^2}{m^2-25}right)=$

$left( frac{m^2}{m+5}- frac{m^3}{(m+5)^2}right):left( frac{m}{m+5}- frac{m^2}{(m+5)(m-5)}right)=$

$left( frac{m^2(m+5)}{(m+5)^2}- frac{m^3}{(m+5)^2}right):left( frac{m(m-5)}{(m+5)(m+5)}- frac{m^2}{(m+5)(m-5)}right)=$

$frac{m^3+5m^2-m^3}{(m+5)^2}: frac{m(m-5)-m^2}{(m+5)(m-5)}=$

$frac{5m^2}{(m+5)^2}: frac{m^2-5m-m^2}{(m+5)(m-5)}=$

$frac{5m^2}{(m+5)^2}: frac{-5m}{(m+5)(m-5)}=$

$frac{5m^2}{(m+5)^2} cdot frac{(m+5)(m-5)}{-5m}=$

$frac{m}{m+5} cdot frac{m-5}{-1}=frac{m(m-5)}{-(m+5)}=frac{m^2-5m}{-(m+5)}= frac{5m-m^2}{m+5}$